В олимпиаде по математике приняли участие 40 студентов, им было предложено решить одну задачу по линейной алгебре, одну по теории множеств и одну по теории вероятности. По линейной алгебре решили задачу 20 человек, по теории множеств – 18 человек, по теории вероятности – 18 человек.
Задачи по линейной алгебре и теории множеств решили 7 человек, по линейной алгебре и теории вероятности – 9 человек. Ни одной задачи не решили 3 человека.
- Сколько учащихся решили все задачи?
- Сколько учащихся решили только две задачи?
- Сколько учащихся решили только одну задачу?
Не уверена 100% в правильности, но предлагаю такое решение:
1. Решили все задачи 0 уч
2. Только две задачи решили 19 уч
3. Только одну задачу решили 18 уч
Задачка с подвохом? Как ее решить если неизвестно сколько учащихся решило одновременно задачи по теории множеств и теории вероятности? :(
На первый взгляд возможны 6 вариантов решения задачи.
3 задачи
2 задачи
1 задача
0 задач
Всего
6
7
24
3
40
5
9
23
3
40
4
11
22
3
40
3
13
21
3
40
2
15
20
3
40
1
17
19
3
40
Не рассматриваю варианты, когда 3 задачи решили 7 человек, либо никто не решил, потому что тогда возникают "нулевые" пересечения множеств. Для себя решила, что это "неправильно".
На самом деле это была таблица)) Но, почему-то она превратилась в сплошной текст.
У задачи не одно решение, естественно , что задача с подвохом. Будет время, постараюсь рассмотреть еще варианты.
Вопрос к ассистенту преподавателя. А какие-либо комментарии по поводу правильности рассуждений студентов предусмотрены или нет? Как, в конечном итоге, мы узнаем правильное решение той или иной задачи?
Юлия, доброе утро!
Спасибо за Ваш вопрос.
Да, чуть позже, когда ответов поступит больше, преподаватель даст обратную связь с комментариями по решениям.
У меня получилось 4 варианта ответа:
Вариант 1:
Сколько учащихся решили все задачи? - 1
Сколько учащихся решили только две задачи? - 20
Сколько учащихся решили только одну задачу? - 13
Вариант 2:
Сколько учащихся решили все задачи? - 3
Сколько учащихся решили только две задачи? - 15
Сколько учащихся решили только одну задачу? - 17
Вариант 3:
Сколько учащихся решили все задачи?- 5
Сколько учащихся решили только две задачи? - 10
Сколько учащихся решили только одну задачу? - 21
Вариант 4:
Сколько учащихся решили все задачи? - 7
Сколько учащихся решили только две задачи? - 5
Сколько учащихся решили только одну задачу? - 25
Могу добавить решение.
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